AIM:

The study of the behavior of a plate having holes under tension or stretching conditions is the main aim of this study.

THEORY:

Stress Concentration:

Stress Concentration is the location of an area of the element where the stress is significantly greater than its surrounding areas. The areas where the stress is concentrated in an element is known as stress concentration. Stress concentrations occur when there are irregularities in the geometry or material of a structural component that cause an interruption to the flow of stress.

Stress Concentration at Holes

The holes are made on any part to satisfy functional requirements, reduce weight, achieve the economic benefits, etc. As holes create an irregularity in geometry, stress concentration often occurs at these holes. The stress concentration might fail the part. This is not desirable in any case. Thus, analysis is run to study the stress concentration and get the FOS of the element. In our case, there are holes on a rectangular metal plate. The plate is stretched from one side while the other side is fixed. Thus, it will result in the stress concentration around the holes due to irregularities in geometry which causes interruption to the flow of stress.

OBJECTIVES:

1. To create a model of a plate having a circular hole at its center and then, run a static analysis.
2. To create a model of a plate having a circular hole at its center and two more holes at a certain distance from the central holes then, run a static analysis.
3. Compare the results and suggest the best one.

COMMON ANALYSIS:

Following are the details of all the analysis: -

Material Selection

The material used for all the analyses is Steel Alloy. The properties of the alloy steel are shown in figure 1.

            Properties of alloy steel.

Case 1 :Static Analysis of plate having a circular hole at its centre.

Procedure: -

The procedure used for the analysis is as follows

1. Create a sketch of the model having a circular hole at its center and extrude it to 30 mm.
2. Start a new study. Under it select Static analysis and name it as the plate with one hole.
3. Apply the Alloy Steel Material
4. Apply the fixtures.
5. Apply the loads
6. Generate a mesh with appropriate parameters.
7. Run the study.

Analysis Setup: -

Model: -

First of all, a sketch was made from the dimensions given below.

• Length = 300mm
• Height = 120 mm
• Thickness = 30 mm.
• A circular hole at the center: Diameter = 60 mm.

Model of the plate.

Fixture: -

The plate was supposed to be fixed at one of the smaller ends of the plate. Figure 5 shows the fixed geometry on the plate.

 Fixed geometry on the plate.

Loads: -

The load was applied to the other smaller face of the plate such that it is stretched. This means that the direction of the force must be outward i.e. the plate is pulled. A load of 1000 N is applied which is shown.

 A 1000 N load applied such that the plate is stretched.

Mesh: -

 The meshed model of the plate with one hole is shown.

 Meshed model of the plate with one hole.

Case1: Analysis Results: -

The analysis results are obtained in terms of strain, stress, and displacement plots.

Von Misses Stress Plot:

The Von Misses Stress plot for the plate with a circular hole at its center. The maximum and minimum stress obtained are 1.199e+06 and 2.743e+04. The maximum stress is obtained at the hole as it is a stress concentration area.

Von Mises stress plot.

Equivalent Strain Plot:

The equivalent strain plot is shown below. The maximum and minimum strain values are 4.537e-06 and 2.209e-07. The  strain is more at the hole of the plate.

Equivalent Strain Plot.

Displacement Plot:

As the plate is stretched from one side, the displacement is shown below

 Displacement Plot.

Case 2: Static Analysis of plate having three circular holes.

Procedure: -

The procedure used for the analysis is as follows

1. Create a sketch of the model having the three holes and extrude it to 30 mm.
2. Start a new study. Under it select Static analysis and name it as the plate with one hole.
3. Apply the Alloy Steel Material
4. Apply the fixtures.
5. Apply the loads
6. Generate a mesh with appropriate parameters.
7. Run the study.

Analysis Setup: -

Model: -

First of all, a sketch was made from the dimensions given below as shown in figure 11.

• Length = 300mm
• Height = 120 mm
• Thickness = 30 mm.
• A circular hole at the center: Diameter = 60 mm.
• Two holes of 30 mm diameter are placed 90mm away from the central hole on both sides.

 Model of the plate.

Fixture: -

The plate was supposed to be fixed at one of the smaller ends of the plate. Figure shows the fixed geometry on the plate.

Fixed Geometry on the plate.

Loads: -

The load was applied to the other smaller face of the plate such that it is stretched. This means that the direction of the force must be outward i.e. the plate is pulled. A load of 1000 N is applied which is shown below

 A 1000 N load applied such that the plate is stretched.

Mesh: -

The meshed model of the plate with one hole is shown below:

 Meshed model of the plate with one hole.

Case 2: Analysis Results: -

The analysis results are obtained in terms of strain, stress, and displacement plots.

Von Misses Stress Plot:

The Von Misses Stress plot for the plate with a circular hole at its center. The maximum and minimum stress obtained are 1.159e+06 and 4.649e+03. The maximum stress is obtained at the central hole similar to that of the previous analysis. The holes are the stress concentration areas.

 Von Mises stress plot.

Equivalent Strain Plot:

The equivalent strain plot is shown below. The maximum and minimum strain values are 4.312e-06 and 1.768e-08. The  strain is more at the central hole of the plate similar to that of the previous analysis.

Equivalent Strain Plot.

Displacement Plot:

As the plate is stretched from one side, the displacement is shown below.

Displacement Plot.

Comparison of Results: -

The results are summarized in a tabular form as shown in table 1. The table contains the details about the stress, strain, and displacement of the plates.

Observation: -

From table 1, it is clear that the stress and strain have decreased in the plate with 3 holes, whereas the displacement has increased. It can also be seen in the stress plots of both cases that the maximum stress occurs at the circular hole and it is indeed a stress concentrated area. In the plate with 3 holes, it can be seen that the stress is more distributed than in the plate with a central circular hole.

Conclusion: -

In this study, two models of a plate were created. One with a single central circular hole and another one with three holes. The static analysis was done on both of them having a 1000 N load on one of its smaller faces. The results obtained showed that the plate with three holes had less stress and strain than the plate with one hole. While the displacement is less than that of the plate with one hole.